We consider the minimal average action (Mather's β function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β-function associated to a standard-like twist map admits a unique C1-holomorphic (canonical) complex extension, which coincides with this function on the set of real diophantine frequencies. In particular, we deduce a uniqueness result for Mather's β function.
On the regularity of Mather's β-function for standard-like twist maps
Carminati C.;
2021-01-01
Abstract
We consider the minimal average action (Mather's β function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β-function associated to a standard-like twist map admits a unique C1-holomorphic (canonical) complex extension, which coincides with this function on the set of real diophantine frequencies. In particular, we deduce a uniqueness result for Mather's β function.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
2003.01402.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
316.21 kB
Formato
Adobe PDF
|
316.21 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.